The most straightforward proofs use algebra or trigonometry to get a formula for the length of the bisector as a function of the sides of the triangle. Geometric proofs are more complicated and require the use of inequalities. If there is no explicit use of inequalities, the proof must rely on some assumption about the position of points in the diagram (such as whether they are inside the triangle or not) and this has led to some false proofs in which the assumption is wrong.